PARAMETER IDENTIFICATION PROBLEMS FOR A CLASS OF STRONGLY DAMPED NONLINEAR WAVE EQUATIONS

S. Nakagiri; J-H. Ha; J. Vanualailai

doi:10.32219/isms.67.3_337

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Keywords: Damped-wave equations, Identification problem, Optimal parameter, Necessary optimality condition, Gâteaux differentiability

JOURNAL FREE ACCESS

2008 Volume 67 Issue 3 Pages 337-352

DOI https://doi.org/10.32219/isms.67.3_337

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Abstract

Parameter identification problems of spatially varying coefficients in a class of strongly damped nonlinear wave equations are studied. The problems are formulated by a minimization of quadratic cost functionals by means of distributive and terminal values measurements. The existence of optimal parameters and necessary optimality conditions for the functionals are proved by the continuity and Gˆateaux differentiability of solutions on parameters.

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